Worksheet – Section 2.7
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1. Find the domain and range of R and R 1 when Rt  
t 3
.
2t  5
2. The life expectancy, L , of a child can be modeled by the function below. The variable y is the year of
birth in relationship to 1980. For example, y  0 corresponds to 1980.
L( y ) 
y  96.94
0.01y  1.3
a. Give a practical interpretation of L(10) . Find the value of L(10)
b. Give a practical interpretation of L1 (78) . Use algebra to find the value of L1 (78) .
3. A manufacturer makes t-shirts and has found that if they charge $20.00 per t-shirt, they will sell 900 tshirts every week. If they drop the price to $17.00 per t-shirt, they will sell 1100 t-shirts.
a. If the quantity of t-shirts sold is a function of the price in which they can sell the t-shirts, find
the linear equation that models this problem. Use p to represent price and q  f ( p ) to
represent quantity sold.
b. Find and interpret f (15).
c. Give a practical interpretation of the slope.
d. Find both the horizontal and vertical intercepts.
e. Give practical interpretations of both of these intercepts.
f. Find the inverse of the equation you found in part A.
g. What does the inverse function tell you, in terms of price and quantity sold?
h. Interpret the slope of the inverse function.
i. Find and interpret f
1
(950).
4.
5. Write the inverse of each of these functions.
a.
b.
, where
and
are constants.